The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds

J. Kurek; W. M. Mikulski

J. Kurek ; W. M. Mikulski

Colloquium Mathematicae, Tome 96 (2003), p. 141-149 / Harvested from The Polish Digital Mathematics Library

Résumé

Let F:ℱ ℳ → ℬ be a vector bundle functor. First we classify all natural operators $T_{p r o j | ℱ ℳ_{m, n}} ⇝ T^{(0, 0)} (F_{| ℱ ℳ_{m, n}}) *$ transforming projectable vector fields on Y to functions on the dual bundle (FY)* for any $ℱ ℳ_{m, n}$ -object Y. Next, under some assumption on F we study natural operators $T *_{h o r | ℱ ℳ_{m, n}} ⇝ T * (F_{| ℱ ℳ_{m, n}}) *$ lifting horizontal 1-forms on Y to 1-forms on (FY)* for any Y as above. As an application we classify natural operators $T *_{h o r | ℱ ℳ_{m, n}} ⇝ T * (F_{| ℱ ℳ_{m, n}}) *$ for some vector bundle functors F on fibered manifolds.

Publié le : 2003-01-01

Zbl 1052.58004

EUDML-ID : urn:eudml:doc:285048

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     title = {The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds},
     journal = {Colloquium Mathematicae},
     volume = {96},
     year = {2003},
     pages = {141-149},
     zbl = {1052.58004},
     language = {en},
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J. Kurek; W. M. Mikulski. The natural operators lifting horizontal 1-forms to some vector bundle functors on fibered manifolds. Colloquium Mathematicae, Tome 96 (2003) pp. 141-149. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-1/